The present disclosure relates to photovoltaic devices, and more particularly to photovoltaic devices including a compositionally-graded band gap heterojunction and methods of forming the same.
A photovoltaic device is a device that converts the energy of incident photons to electromotive force (e.m.f.). Typical photovoltaic devices include solar cells, which are configured to convert the energy in the electromagnetic radiation from the Sun to electric energy. Each photon has an energy given by the formula E=hν, in which the energy E is equal to the product of the Plank constant h and the frequency ν of the electromagnetic radiation associated with the photon.
Referring to FIG. 1, the functionality of a photovoltaic device can be approximated by an equivalent circuit that includes a current source, a diode, and two resistors. The circuit of FIG. 1 approximates a unit area of a physical photovoltaic device, which provides electrical current that is proportional to the total irradiated area of the physical photovoltaic device. The photovoltaic current per unit area generated by the physical photovoltaic device is referred to as a short-circuit current density Jsc, i.e., the current density generated by the physical photovoltaic device if the positive node and the negative node of the physical photovoltaic device are electrically shorted. Thus, the current source in FIG. 1 generates an electrical current with a current density of the short-circuit current density Jsc.
Power dissipation through internal leakage current is approximated by a shunt resistance Rsh. A finite value for the shunt resistance Rsh triggers an internal leakage current through a physical photovoltaic device, and degrades the performance of the physical photovoltaic device. The lesser the shunt resistance Rsh, the greater is the internal power loss due to the internal leakage current.
Power dissipation through internal resistance of the physical photovoltaic device is approximated by a series resistance Rs. A non-zero value for the series resistance Rs triggers Joule loss within the physical photovoltaic device. The greater the series resistance Rs, the greater is the internal power loss due to the internal resistance of the physical photovoltaic device.
The potential difference between the positive node and the negative node of a photovoltaic device generates an internal current that flows in the opposite direction to the photocurrent, i.e., the current represented by the current source having the short-circuit current density Jsc. The dark current has the same functional dependence on the voltage across the current source as a diode current. Thus, the dark current is approximated by a diode that allows a reverse-direction current. The density of the dark current, i.e., the dark current per unit area of the physical photovoltaic device, is referred to as the dark current density Jdark. An external load can be attached to an outer node of the series resistor and one of the nodes of the current source. In FIG. 1, the value the impedance of the load is the value of the actual impedance of a physical load is divided by the area of the physical photovoltaic cell because the equivalent circuit of FIG. 1 describes the functionality of a unit area of the physical photovoltaic cell.
Referring to FIG. 2, a schematic graph of an I-V curve of a physical photovoltaic device structure is shown. The bias voltage V is the voltage across the load in the equivalent circuit of FIG. 1. The open circuit voltage Voc corresponds to the voltage across the load as the resistance of the load diverges to infinity, i.e., the voltage across the current source when the load is disconnected. The inverse of the absolute value of the slope of the I-V curve at V=0 and J=Jsc is approximately equal to the value of the shunt resistance Rsh. The inverse of the absolute value of the slope of the I-V curve at V=Voc and J=0 is approximately equal to the value of the series resistance Rs. The effect of the dark current is shown as an exponential decrease in the current density J as a function of the bias voltage V around a non-zero value of the bias voltage.
The operating range of a photovoltaic device is the portion of the I-V curve in the first quadrant, i.e., when both the bias voltage V and the current density J are positive. The power density P, i.e., the density of power generated from an unit area of the physical photovoltaic device of FIG. 1, is proportional to the product of the voltage V and the current density J along the I-V curve. The power density P reaches a maximum at a maximum power point of the I-V curve, which has the bias voltage of Vm and the current density of Jm. The fill factor FF is defined by the following formula:
                    FF        =                                                            J                m                            ×                              V                m                                                                    J                sc                            ×                              V                oc                                              .                                    (                  Eq          .                                          ⁢          1                )            The fill factor FF defines the degree by which the I-V curve of FIG. 3 approximates a rectangle. The fill factor FF is affected by the series resistance Rs and the shunt resistance Rsh. The smaller the series resistance Rs, the greater the fill factor FF. The greater the shunt resistance Rsh, the greater the fill factor FF. The theoretical maximum for the fill factor is 1.0.
The efficiency η of a photovoltaic device is the ratio of the power density at the maximum power point to the incident light power density Ps. In other words, the efficiency η is given by:
                    η        =                                                            J                m                            ×                              V                m                                                    P              s                                .                                    (                  Eq          .                                          ⁢          2                )            Eq. 2 can be rewritten as:
                    η        =                                                            J                sc                            ×                              V                oc                            ×              FF                                      P              s                                .                                    (                  Eq          .                                          ⁢          3                )            Thus, the efficiency h of a photovoltaic device is proportional to the short circuit current density Jsc, the open circuit voltage Voc, and the fill factor FF.
The efficiency η of a photovoltaic device depends on the spectral composition of the incident light. For solar cells, the efficiency is calculated under a standard radiation condition defined as 1 sun, which employs the spectrum of the sunlight.
As Eq. 3 indicates, the efficiency η of a photovoltaic device is proportional to the product of the short circuit current density Jsc and the open circuit voltage Voc. In order to enhance the efficiency η of a photovoltaic device, therefore, it is necessary to increase the product of the short circuit current density Jsc and the open circuit voltage Voc.